On the Convergence of an Interpolatory Product Rule for Evaluating Cauchy Principal Value Integrals

Criscuolo, G.; Mastroianni, G.

doi:10.2307/2007839

Cited by 16 publications

(28 citation statements)

References 4 publications

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“…All known estimates refer to a variable y bounded away from the endpoints ±1 (see for example [3], [12]). In this paper we derive for (1.2) a pointwise error estimate which, taking into account property (1.4), will then allow us to obtain a bound for the global term (1.6).…”

Section: Introductionmentioning

confidence: 99%

Error estimates in the numerical evaluation of some BEM singular integrals

Mastroianni

Monegato

2000

Math. Comp.

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Abstract. In some applications of Galerkin boundary element methods one has to compute integrals which, after proper normalization, are of the formIn this paper we derive error estimates for a numerical approach recently proposed to evaluate the above integral when a p−, or h − p, formulation of a Galerkin method is used. This approach suggests approximating the inner integral by a quadrature formula of interpolatory type that exactly integrates the Cauchy kernel, and the outer integral by a rule which takes into account the log endpoint singularities of its integrand. Some numerical examples are also given.

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Section: Introductionmentioning

confidence: 99%

Error estimates in the numerical evaluation of some BEM singular integrals

Mastroianni

Monegato

2000

Math. Comp.

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“…For calculating integrals as (4.13) we will use quadrature rules of the following types: 16) where 0 ≤ x 1 < x 2 < ··· < x m ≤ 2π , and 17) where…”

Section: Approximate Methods Of the Calculation Of The Polysingular Imentioning

confidence: 99%

“…The results on the Gaussian quadrature rules can be found in [17,20,21,22,25]. On the other hand, the integral K[f , t] can be represented as (1.39).…”

Section: N− 1 and Is Denoted Byf (T)mentioning

confidence: 99%

Numerical methods of computation of singular and hypersingular integrals

Boikov

2001

International Journal of Mathematics and Mathematical Sciences

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Abstract. In solving numerous problems in mathematics, mechanics, physics, and technology one is faced with necessity of calculating different singular integrals.In analytical form calculation of singular integrals is possible only in unusual cases. Therefore approximate methods of singular integrals calculation are an active developing direction of computing in mathematics. This review is devoted to the optimal with respect to accuracy algorithms of the calculation of singular integrals with fixed singularity, Cauchy and Hilbert kernels, polysingular and many-dimensional singular integrals. The isolated section is devoted to the optimal with respect to accuracy algorithms of the calculation of the hypersingular integrals.

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“…However, if we assume that the Dini type condition In the last decade several papers have dealt with the numerical approximation of the Hilbert Transform in the case of bounded intervals and the reader can refer to [4], [5], [6], [7], [13] [18], [20], [25] and [26]. The algorithms proposed in these papers are mainly two: Gauss-type quadrature rules and product quadrature rules.…”

Section: G(x) X − T Dx = Limmentioning

confidence: 99%